Fractions


Adding Mixed Numbers

When Mixed Numbers are added, those Mixed Numbers must first be changed to Improper Fractions.







Adding Mixed Numbers with Like Denominators




1
3
8

+

2
1
8




Change these Mixed Numbers to Improper Fractions.


11
8

+
17
8




To add these Fractions, first add the Numerators.

The sum of the Numerators becomes the new Numerator.

The Denominator remains the same.



11
8

+
17
8

=
28
8




If the answer results in an ImproperFraction, then change that Improper Fraction to a Mixed Number.




28
8

=

3
4
8




If the resulting Proper Fraction can be reduced, then do so.





3
4
8

=

3
1
2







Adding Mixed Numbers with Unlike Denominators




2
1
3

+

1
1
2




Change these Mixed Numbers to Improper Fractions.


7
3

+
3
2




Find the Least Common Denominator.


7
3

=
14
6



3
2

=
9
6



14
6

+
9
6




With Like Denominators, the Numerators, can be added.

The sum of the Numerators becomes the new Numerator.

The Denominator remains the Least Common Denominator.



14
6

+
9
6

=
23
6




If the answer results in an ImproperFraction, then change that Improper Fraction to a Mixed Number.




23
6

=

3
5
6





RULE

Adding Mixed Numbers


Change the Mixed Numbers to Improper Fractions.

Change any Unlike Denominators to Like Denominators.

Add the Numerators. Keep the Common Denominator.

If the Proper Fraction can be Reduced, then do so.

If the answer is an Improper Fraction, then change it to a Mixed Number.